It's hard to say on the alertness/working memory part. I regularly use the Dual-N-Back test to measure/imporve my working memory, and the best results I've had have been immediately after using TDCS, but the effect is a subtle one.
That said, one of the side benefits (and which is more predicatable and tangible) is that your mood seems to improve: The day after I use TDCS I feel happier/lighter. From my perspective it is worth continuing to use it for this alone.
There are a few tricks on getting the right electrode placement (this also determines the type of effect TDCS wuill have) and the skin beneath the electrodes can be a bit irritated after 15 minutes, but apart from that I'd recommend it to anyone.
I've tried it, but I wouldn't use the circuit they describe here. If you did you'd get 5mA or more out of the battery and that would be most unpleasant on your skin if you kept it up for more than a couple of minutes.
You'll need a resistor in series with the battery to limit the current (or a pot, for better accuracy/tuning). If you put a 4.7k in series at least you know that you won't be putting more that 2mA through. In my experience, your head (through two wet sponge electrodes) has a resistance of about 2kOhm.
If you've got a multimeter then I'd use that as well to verify how much current is going through your head.
I have to admit, my attention to my work always improves right after I get a good shock by touching the wrong wire. I suspect that the electric current stimulates the adrenal gland, which would make you both attentive and alert. The downside would be the bodies reaction to excessive adrenalin surges. Those have been known to kill people.
Still, it could be worth some expirementation with medical supervision.